Question

In an AP, Sum of the 10 terms is 180 and last term is 28, then Find first term.

Answer 1

Let l be the last term = 28

Sum of the 10 terms is =180

28 = a+(n-1) d

28= a +9d -----------(i)

and S=180

$\Rightarrow$ 180=$\frac{n}{2}$ [ 2a+(n-1) d]

$\Rightarrow$ 180 =$\frac{10}{2}$ [ 2a + 9d]

$\Rightarrow$ 36 = 2a+ 9d -------------(ii)

Solving equations (i) and (ii), we get

$\Rightarrow$ a =8